Finite-Dimensional Quantum Model For The Stock Market, Discrete Nature Of The Quantities Used In Finance, Spectral Representation Of Bessel Processes With Constant Drift, Credit Spreads, And Stochastic Volatility In Finance, Quantum Structure In Cognition
Following structural and syllogistical confederational concatenation is studied with concomitant and consummative properties: Finite-Dimensional Quantum Model For The Stock Market, Discrete Nature Of The Quantities Used In Finance, Spectral Representation Of Bessel Processes With Constant Drift, Credit Spreads, And Stochastic Volatility In Finance, Quantum Structure In Cognition, Non Classicality Of The Membership Weight Structure, Minimal Length Uncertainty And The Quantum Model For The Stock Market, Superpositions Of Probability Distributions, Quantum Finance: The Finite Dimensional Case, Foreign Exchange Market As A Lattice Gauge Theory, Classical Logical Versus Quantum Conceptual Thought, Adaptive-Wave Alternative For The Black-Scholes Option Pricing Model Key words: Spectral Representation Of Bessel Processes, Quantum Conceptual Thought, Black-Scholes Option Pricing Model, Black-Scholes Option Pricing Model, Quantum Structure In Cognition The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-648791-654990.pdf
Following structural and syllogistical confederational concatenation is studied with concomitant and consummative properties: Finite-Dimensional Quantum Model For The Stock Market, Discrete Nature Of The Quantities Used In Finance, Spectral Representation Of Bessel Processes With Constant Drift, Credit Spreads, And Stochastic Volatility In Finance, Quantum Structure In Cognition, Non Classicality Of The Membership Weight Structure, Minimal Length Uncertainty And The Quantum Model For The Stock Market, Superpositions Of Probability Distributions, Quantum Finance: The Finite Dimensional Case, Foreign Exchange Market As A Lattice Gauge Theory, Classical Logical Versus Quantum Conceptual Thought, Adaptive-Wave Alternative For The Black-Scholes Option Pricing Model Key words: Spectral Representation Of Bessel Processes, Quantum Conceptual Thought, Black-Scholes Option Pricing Model, Black-Scholes Option Pricing Model, Quantum Structure In Cognition The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-648791-654990.pdf
We study the following system consummatory and concatenational and investigate its properties: Exact Solutions For Optimal Execution Of Portfolios Transactions And The Riccati Equation, Schr Odinger Group, Quantum Finance And Bipartite Quantum Coherence In Noninertial Frames, Quantum Finance, Relativistic Quantum Econophysics - New Paradigms In Complex Systems Modelling, Statistical Mechanics And Its Applications In Quantum Finance, Temporal Evolution Of An Isolated Market Is Unitary In Hilbert Space, Quantum Financial Economics, Financial Market Modeling With Quantum Neural Networks And Multiple Round Evolutionary Quantum Game Equilibrium, Heisenberg Uncertainty Principle And Economic Analogues Of Basic Physical Quantities, Randomness Confidence Bands Of Fractal Scaling Exponents For Financial Price Returns, Quantum Brownian Motion Model For The Stock Market, Spatial Interactions In Agent-Based ModelingKey Words: Complex Systems Modelling, Econophysics, Quantum Neural Networks, Agent-Based Modeling, Quantum Finance, Riccati Equation, Schr Odinger Group The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-623335-629538.pdf
Following system is investigated with its corresponding properties in detail: A Quantum Model Of Option Pricing: When Black–Scholes Meets Schrödinger And Its Semi-Classical Limit, Black–Scholes Option Pricing Model In A More General Quantum Physics Setting, Perfect Market Equilibrium State Postulated By The Black–Scholes Model Represents A Particular Case., Controlled Markov Processes And Mathematical Finance, Controlled Markov Processes And Mathematical Finance, Dynamic Optimization And Its Relation To Classical And Quantum Constrained Systems, Consistency Relation, Inter-Occurrence Times And Universal Laws In Finance, Earthquakes And Genomes, Quantum Cognition Beyond Hilbert Space Ii, Quantum Master Equation For Long-Term Prognosis.. The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-654991-661307.pdf
Models are given with concomitant properties for the following concatenated system: Dynamical Systems, Causation Entropy From Symbolic Representations Of Dynamical Systems, Quantum Cognition Based On An Ambiguous Representation, Expression Of Apprehension And Judgment, Basic Cognitive Process Of Decision Making, As An Inverse Bayes Inference Classifying The Information Content Of Neuron Spike Trains, A Priori And A Posteriori Hypotheses In Bayes Inference Are Replaced By The Upper And Lower Approximations, Logical Structure Of Such Combined Approximations Can Only Be Expressed As An Orthomodular Lattice And Therefore Can Be Represented By A Quantum Rather Than A Boolean Logic, Apprehension We Understand The Coherent Perception Correlated With The Recruitment And Engagement In Collective Behavior Of The Required Neuronal Populations, Quantum-Like Behavior In Language, Concep The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-680007-686491.pdf
Abstract: The limitations of the classical Black-Scholes model are examined by comparing calculated and actual historical prices of European call options on stocks from several sectors of the S &P 500. Persistent differences between the two prices point to an expanded model proposed by Segal and Segal (PNAS 95:4072-4075, 1988) in which information not simultaneously observable or actionable with public information can be represented by an additional pseudo-Wiener process. A real linear combination of the original and added processes leads to a commutation relation analogous to that between a boson field and its canonical momentum in quantum field theory. The resulting pricing formula for a European call option replaces the classical volatility with the norm of a complex quantity, whose imaginary part is shown to compensate for the disparity between prices obtained from the classical Black-Scholes model and actual prices of the test call options. This provides market evidence for the influence of a non-classical process on the price of a security based on non-commuting operators. Supplementary Information: The online version contains supplementary material available at 10.1140/epjb/s10051-022-00402-0.
Abstract Finance stands as the most quantitatively advanced branch of the social sciences, yet it is also the most humbling. The mean-variance efficient frontier, the CAPM, arbitrage pricing relations, the Black–Scholes–Merton option formula and the efficient market hypothesis possess unparalleled formal elegance, yet they suffered a broad empirical refutation in the global financial crisis of 2008. Standard models understate tail risk, misinterpret the comovement of assets that are supposed to diversify risk, and presuppose liquidity and rationality — two features that vanish precisely when they are most needed. Behavioural finance has documented an extensive catalogue of cognitive biases, yet it remains a patchwork of isolated effects without a unified calculus of probability. This monograph is the first systematic work to establish quantum finance. It argues that the mathematical formalism of quantum mechanics supplies this missing unified structure: financial states are state vectors in Hilbert space; beliefs and valuations coexist as superposed amplitudes; trading and information disclosure act as measurements that collapse states in accordance with the Born rule; assets and markets are entangled with one another; and path interference generates fat tails and herding, which are inadmissible under classical additive probability. The book comprises six parts and thirty chapters in total. Part I lays the philosophical and formal foundations. Starting from the paradigm crisis, it proceeds through quantum probability and quantum stochastic processes to construct the analytical framework built on three core pillars of quantum finance. Part II develops quantum asset pricing, covering the quantum CAPM, quantum APT, quantum option pricing and the term structure of interest rates. Part III advances quantum risk management, including quantum risk measures, Value-at-Risk (VaR) and expected shortfall, stress testing, credit risk and phase transitions in systemic risk. Part IV addresses quantum portfolios and asset allocation, ranging from the quantum meanvariance frontier, strategic and tactical asset allocation, to factor investing and hedge fund strategies. Part V turns to market microstructure and behavioural finance, examining quantum order flows, marketmaker liquidity, quantum prospect theory and market sentiment. Part VI looks ahead to frontier avenues: quantum computational optimization, quantum machine learning, blockchains, postquantum cryptography and quantuminformed financial regulation. This book rigorously recovers the classical CAPM, efficient market hypothesis and Gaussian risk models as special cases under decoherence limits. It is intended for graduate students and faculty in finance and financial engineering, as well as researchers and practitioners working on asset pricing, risk management, portfolio allocation and financial regulation.
Adaptive wave model for financial option pricing is proposed, as a high-complexity alternative to the standard Black--Scholes model. The new option-pricing model, representing a controlled Brownian motion, includes two wave-type approaches: nonlinear and quantum, both based on (adaptive form of) the Schr\odinger equation. The nonlinear approach comes in two flavors: (i) for the case of constant volatility, it is defined by a single adaptive nonlinear Schr\odinger (NLS) equation, while for the case of stochastic volatility, it is defined by an adaptive Manakov system of two coupled NLS equations. The linear quantum approach is defined in terms of de Broglie's plane waves and free-particle Schr\odinger equation. In this approach, financial variables have quantum-mechanical interpretation and satisfy the Heisenberg-type uncertainty relations. Both models are capable of successful fitting of the Black--Scholes data, as well as defining Greeks.
Keywords: Black--Scholes option pricing, adaptive nonlinear Schr\odinger equation, adaptive Manakov system, quantum-mechanical option pricing, market-heat potential
PACS: 89.65.Gh, 05.45.Yv, 03.65.Ge